0 votes 0 votes One way of classification of compound prepositions on the basis of their truth values as per Kenneth H Rosen is Tautology Contradiction Contingency Then in which classification validity and satisfiability are used? Mathematical Logic propositional-logic + – Mk Utkarsh asked Feb 7, 2018 edited Feb 7, 2018 by Mk Utkarsh Mk Utkarsh 984 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Valid means if the statement is true for all combinations. We use satisfiable if we have may statements like "A" AND "B" AND "C" Now, "A" AND "B" AND "C" =true if A, B and C is true .Here we have atleast 1 combination that is true Angkit answered Feb 10, 2018 edited Feb 10, 2018 by Angkit Angkit comment Share Follow See all 9 Comments See all 9 9 Comments reply Show 6 previous comments Mamta Satywali commented Feb 11, 2018 reply Follow Share In logic, a tautology is a formula or assertion that is true in every possible interpretation. Check here-https://en.wikipedia.org/wiki/Tautology_(logic) A formula is valid if all interpretations make the formula true. Check here-https://en.wikipedia.org/wiki/Satisfiability In logic, contingency is the status of propositions that are neither true under every possible valuation (i.e. tautology) nor false under every possible valuation (i.e. contradiction). Check here-https://en.wikipedia.org/wiki/Contingency_(philosophy) A formula is satisfiable if it is possible to find an interpretation that makes the formula true. Check here-https://en.wikipedia.org/wiki/Satisfiability Final Conclusion- Tautology implies Validity only. Contingency implies Satisfiability. 0 votes 0 votes Angkit commented Feb 11, 2018 reply Follow Share Content is fine but please read this once : https://math.stackexchange.com/questions/258602/what-is-validity-and-satisfiability-in-a-propositional-statement 0 votes 0 votes Mamta Satywali commented Feb 11, 2018 reply Follow Share Correct, Whatever which is tautology is Satisfiable/Contingency. My aim is to fit them into defined classification as the question demands so- Wouldn't it be better to classify Satisfiable propositions into Contingency which is already defined in classification (as obviously contingency is there for a specific purpose which in turn includes all propositions that are in tautology)? As I said before, Tautology is equivalent to Validity and Contingency is equivalent to Satisfiability. Tautology may imply Satisfiability but can never be equivalent to it. Hope I made my point clear now. 0 votes 0 votes Please log in or register to add a comment.